Simple carbon steels are less wear-resistant (or 'abrasion-resistant'), due to a lack of the elements that add wear resistance in the form of carbides, like chromium, vanadium, tungsten, etc. But in terms of 'hardness', as the term is applied to steels in general, that's usually more about heat treat than wear resistance, and it describes the ability of the steel to resist deformation, like edge-rolling or denting, etc. In other words, a carbon blade that's inherently less wear-resistant can still be made 'harder' (by heat treat) than a more wear-resistant 'super steel' heat-treated more conservatively; in that case, the carbon steel blade would be less-prone to deformation (rolling, etc). A simple carbon blade in 1095 can be hardened to 62 HRC, which would be harder than a blade of S30V, D2, etc at 58 HRC. But in terms of wear resistance, the 1095 blade would still be lacking in that, and would respond more easily to abrasive stropping (honing, thinning, polishing) than would the 'super steel' at even a lower hardness.
Stropping, in the classic sense of 'realigning' an edge that's lightly rolled, is more effective with steels heat-treated to a lower hardness, because they're more prone to deformation, which includes 'deforming' a rolled edge to be aligned straight again. Those could be either simple carbon steels, low- or mid-alloy stainless (like the Swedish steels) or they could also be 'super steels' that aren't heat-treated to extreme hardness. If 'stropping' is done with a polishing compound, with the goal of additional honing, thinning or polishing of the edge, then it could be more effective on any steel at any hardness using a compound appropriate to the steel, i.e., able to polish or shape it's carbides.
All this is to say, a simple carbon steel straight razor heat-treated to higher hardness could be less-prone to edge rolling (i.e., 'harder'), and therefore require less stropping than a 'super steel' which isn't heat-treated to as high a hardness. Carbon steel won't always be 'softer' than the super steels, in other words. That depends on how each is heat-treated, so either one could be harder, or they could be equally hard. But the simple carbon steel will always be less wear-resistant than the super steels, due to the difference in carbide content between them.
Whether stropping works better for one or the other depends on the heat-treated hardness, or the wear resistance, or both of those things in tandem, depending on what's used to do the stropping (with abrasives, or without them) and what the goal of stropping is (simple realignment vs. honing/thinning/polishing).